given the points a(-3 -5) and b(5,0), find the coordinates off point P that is 2/5 of the way along the directed line segment AB

Accepted Solution

Answer:[tex](\frac{1}{5}, -3)[/tex]Step-by-step explanation:The point P is at [tex]\frac{2}{5}[/tex] of the way along the directed line segment AB. So, If segment AB = x units then P will be at [tex]\frac{2x}{5}[/tex] distance from A along AB direction.That means point P divides the line segment AB in the ratio [tex]\frac{2x}{5} : (x - \frac{2x}{5})[/tex] ≑ [tex]\frac{2x}{5} : \frac{3x}{5}[/tex] ≑ 2 : 3 internally.If point A is (-3,-5) and point B is (5,0) then the coordinates of point P will be given by [tex](\frac{-3 \times 3 + 5 \times 2}{2 + 3},\frac{-5 \times 3 + 0 \times 2}{2 + 3} ) = (\frac{1}{5}, -3)[/tex] (Answer)We know the formula for the coordinates of any point that divide the line segment between the given two point ([tex]x_{1}, y_{1}[/tex]) and ([tex]x_{2}, y_{2}[/tex]) in the ratio m : n internally is given by [[tex]\frac{x_{1}\times n + x_{2} \times m Β }{m + n}, \frac{y_{1}\times n + y_{2} \times m Β }{m + n}[/tex]].